Inertial sensors are variously called seismometers, accelerometers, tiltmeters, gravimeters and geophones. The naming differs primarily according to the field of application. However with all of these types of sensor the common element is the detection of ground motion by sensing the motion of an inertial mass. A suspension mechanism typically consists of one or more leaf springs, called flexure elements or simply flexures, serves to constrain the motion of the inertial mass and balance the effect of gravity and typically provides a restoring force to the inertial mass.
FIG. 1 is a graph to illustrate a limitation on the sensitivity of an inertial sensor: the background shaking of the earth itself, commonly called the new low-noise model 17 or NLNM. A typical noise spectrum at a well-designed seismic vault can be many orders of magnitude higher than this, but will very rarely dip below the NLNM. The peak between 0.1 and 1 Hz is known as the microseismic peak. Frequencies below the microseismic peak are known as the long-period band of the seismic spectrum.
The ability of an inertial sensor to measure ground motion is impaired by its own internally generated noise. The internal noise level of an inertial sensor depends, among other things, on dimensional stability of the suspension mechanism that supports the inertial mass, and this is particularly critical at low frequencies. There are two types of long-period internal noise that are of particular concern: creep noise and hysteresis noise.
Flicker noise, variously called pink noise or 1/f noise, is found at low frequencies in most physical phenomena. Mechanical flicker noise in a pendulum is related to temperature and to the lossiness of the suspension. Because of the latter relationship—it will be referred to as hysteresis noise. Suspension hysteresis, also known as anelasticity, is quantified by measuring the phase shift between applied stress and resulting strain, called the loss angle. A hysteresis noise spectrum 18 at the level of the NLNM corresponds to a loss angle on the order of 3×10−4 radians.
Sudden spontaneous changes in the apparent output acceleration of an inertial sensor relate to small changes in the tilt of the frame or to small displacements of the inertial mass. Because of the characteristic noise spectrum associated with these “pops” or “glitches” it is variously called red noise or 1/f2 noise; however, because of its origin it will be referred to as creep noise. In order to have a spectrum below the NLNM the square root of the sum of the squares of any spontaneous displacements should be less than approximately 0.25 nm in any hour. This level of creep noise 19 is also shown on FIG. 1.
A third source of noise is due to the fact that the earth is constantly moving in three axes of translation and three axes of rotation. A sensor should have a well-defined sensitive axis and have low off-axis sensitivity; otherwise off-axis ground motion will appear as noise. If the inertial mass is constrained to be more compliant in one axis than in any other it can be said to have a single effective degree of freedom.
If the instrument's ability to detect small signals at low frequencies is sufficient it becomes apparent that the sensor performance is limited by the three factors described above, among others. A long-period weak-motion inertial sensor is defined as one that can resolve signals below −160 dB with respect to 1 m2/s3 at frequencies below 0.1 Hz. At higher frequencies and amplitudes, the small spontaneous displacements and hysteresis loss described above cease to be a concern.
One approach to the design of long-period weak-motion inertial sensor suspensions is to use flat metal leaf springs, which are clamped with separate clamp pieces to the frame and movable mass of the inertial seismometer. This approach can have the following disadvantages:                As the flexing element changes shape it moves with respect to the clamp holding it. This interaction between the clamp and the flexing element will have a stick-slip characteristic, resulting in hysteresis noise;        Stresses induced by assembly or temperature changes can cause stresses at the clamp-flexure interface that are subsequently released as creep noise;        The clamps add cost in terms of parts count; and        Clamp edge alignment can significantly increase assembly time.        
Another approach is to braze, weld or glue leaf springs to fixed and movable parts to form sub-assemblies which are in turn clamped, press-fit, shrink fitted or otherwise attached to the frame and movable mass. This approach can have the following disadvantages:                It is difficult to inspect and correct small voids in the joints between the leaf springs and fixed and movable pieces. Such voids can cause stick-slip friction and therefore hysteresis and/or creep noise;        Brazing materials and glue can have low yield strength and high loss angle resulting in high hysteresis noise;        Brazing and welding can cause localized high stresses in the part which are subsequently released as creep noise;        Such sub-assemblies are expensive as they typically require very specialized processes to manufacture;        
A third approach is to construct the movable mass, suspension and frame as a monolithic structure. The movable mass is relatively large to keep the sensor self-noise low and relatively complex geometries are needed to keep the off-axis sensitivity low. To achieve these ends in an entirely monolithic structure is very costly. If creep and hysteresis noise can be minimized by some other approach then the expense is unnecessary.
There is a need to provide inertial sensors having suspension mechanisms that address at least some of the previously recited disadvantages.